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attashe74 [19]
3 years ago
5

Dylan has a bank that sorts coins as they are dropped in. The panel on the front shows that there is a value of $17.55 inside of

the bank.
Dylan only collects dimes and quarters. If the number of quarters he has is nine less than twice the amount of dimes, write an equation that can be used to model this equation.
Mathematics
1 answer:
horsena [70]3 years ago
7 0

Answer: .10d+.25q=17.50

d+q=90

10d+10q=900

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a cuboid with a volume of 924 cm3 has dimensions 4cm (x+1)cm and (x+11)cm. show clearly that x^2 +12x-220=0. show the equation b
nikdorinn [45]

Answer:

Part 1)

The equation by factorization is

x^{2}+12x-230=(x-(-6+\sqrt{266}))(x-(-6-\sqrt{266}))

Both values of x are

x1=-6+\sqrt{266}

x2=-6-\sqrt{266}

Part 2) The dimensions of the cuboid are

4\ cm, (-5+\sqrt{266})\ cm and (5+\sqrt{266})\ cm

Step-by-step explanation:

step 1

we know that

The volume of the cuboid is equal to

V=LWH

substitute the given values

V=4(x+1)(x+11)

V=924\ cm^{3}

so

4(x+1)(x+11)=924\\4(x^{2}+11x+x+11)=924\\ 4(x^{2}+12x+11)=924\\x^{2}+12x+11=231\\x^{2}+12x-230=0

Complete the square

x^{2}+12x-230=0

x^{2}+12x=230

x^{2}+12x+36=230+36

(x+6)^{2}=266

square root both sides

x+6=(+/-)\sqrt{266}

x=-6(+/-)\sqrt{266}

so

x1=-6+\sqrt{266}

x2=-6-\sqrt{266}

therefore

The equation by factorization is

x^{2}+12x-230=(x-(-6+\sqrt{266}))(x-(-6-\sqrt{266}))

step 2

Find the dimensions of the cuboid

The dimensions are

4\ cm

(x+1)\ cm -----> (-6+\sqrt{266}+1)=(-5+\sqrt{266})\ cm

(x+11)\ cm ----> (-6+\sqrt{266}+11)=(5+\sqrt{266})\ cm

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Step-by-step explanation:

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